I, like a lot of technically minded-people it seems, like a good crime thriller. Having spent a year mesmerised by Sara Lund's sweaters I picked up The Girl with the Dragon Tattoo. It's a good story, but a bit contrived with the plot being resolved by unexplained and unbelievable computer hacking.

So why write about it on a blog about science and finance?

The plot is set in the context of our hero, a journalist, Blomkvist and his relationship between two businessmen, Wennerström and Vanger. Blomkvist publishes a story claiming Wennerström was involved in a fraud, which he failed to corroborate and the novel begins with his conviction for libel. This makes him vulnerable to an approach from Vanger to investigate the mysterious disappearance of his niece in the 1960s, which is the central mystery in the novel.

What I find interesting is how the different businessmen are presented. Wennerström has become a billionaire from nowhere, building his wealth by participating in such unsavoury activities as options trading and currency speculation. Vanger, on the other hand, is old-money - a traditional industrialist whose family had arrived in Sweden with Napoleon's puppet king, Jean-Baptiste Bernadotte, and was granted land holdings on which they developed paper mills that spawned a firm involved in manufacturing, technology and the media. Within this setting the message is clear: Vanger may be an unpalatable capitalist but Wennerström is beyond the pale.

The sub-text is physiocratic, the Vagner's are legitimate capitalists because they hold land. Wennerström, who has made his own money through speculation, by judgement and foresight, is corrupt. The irony that the hero Blomkvist becomes rich by speculating, that Wennerström is a crook, is passed by. A second irony is that if the events described in the book had actually occurred in England, they might have become of interest to the Leveson Inquiry, looking at actual cases of the relationship between journalists and private detectives involved in phone hacking.

The theme of the corruption of finance is not new, but the novel ignores St Augustine's observation that if a merchant was a cheat, the fault was with the individual, not the profession. What is disturbing is the deep conservatism of the books' sub-text: if some thug in history had not given your ancestors land, you do not deserve to be rich.

I finished reading this book the weekend that France and Germany looked to solve the Euro crisis and impose tighter regulations on financial services. The French President, commenting on the UK's withdrawal from the process, went on to say that "a good part of the world's problems come from the deregulation of financial services".

Both the UK's FSA's, in their recent report on the collapse of RBS, and the US's Financial Crisis Inquiry Commission (FCIC) observe that the regulations existed, but they were not effectively implemented. The UK-US crisis was a failure of government agencies, at the behest of politicians, to enforce rules. The Euro crisis has similar roots in a failure to enforce rules on sovereign debt ratios. The crises seem to have less to do with bankers and more to do with the profligacy of politicians.

Much of the narrative of the ongoing financial crises has been about the imbalance, particularly in the UK, between manufacturing, represented by Vanger, and financial services, the Wennerströms. Implicit is that manufacturing, creating physical objects, is something more real than financial services, moving money around, and moreover, more reputable.

This bias seems to be reflected in UK government science policy. In the recently published Innovation and Research Strategy, the government identifies the following, key, technology based sectors: life sciences, high-value manufacturing, nanotechnology and digital technology. Financial services, while contributing around 10% of UK's GDP, is not mentioned. This approach ignores the advice from the Royal Society in their 2009 report Hidden Wealth.

I would argue that the recent financial crises are about a general lack of understanding of modern finance that enabled institutions to behave irresponsibly. It is hardly surprising that this situation has arisen given the blindness to policy-makers to investing in fundamental research into finance and its underpinning technologies, whether they be the contracts traded, the mathematical models and their computational implementations. This aversion to understanding finance will persist as long as popular culture is dominated by the Vanger=good, Wennerström=bad model.

Thursday, 8 December 2011

David K Waltz has made a comment on my last post, I realised my response was going to be a bit longer than a "comment".

David raises the spectre of the South Sea Bubble and Tuplipmania. I am not an expert on the Tulip Bubble, but I am aware that there is a question as to whether it was a significant as popular imagination suggests (i.e Dumas's The Black Tulip).

The South Sea Bubble (1720) can tell us a lot. In the aftermath the British constitution was completely overhauled - the introduction of the position of Prime Minister (held by Walpole,still the longest serving Prime Minister) was the most obvious impact. In addition, British public finance was put on a firm footing that laid the foundation of successive military victories and the Empire. France's response to the Mississippi Bubble (1719) was less dramatic (they blamed the financier Law) and the consequence was a succession of military defeats.

A tradesman's books are his repeating clock, which upon all occasions are to tell him how he goes on, and how things stand with him in the world: there he will know when it is time to go on, or when it is time to give over; and upon his regular keeping, and fully acquainting himself with his books, depends at least the comfort of his trade, if not the very trade itself. If they are not duly posted, and if every thing is not carefully entered in them, the debtor's accounts kept even, the cash constantly balanced, and the credits all stated, the tradesman is like a ship at sea, steered without a helm; he is all in confusion, and knows not what he does, or where he is; he may be a rich man, or a bankrupt-for, in a word, he can give no account of himself to himself, much less to any body else.

This contrasts with the Rape of Lady Credit by stock-jobbers that Defoe described in 1709

The first Violence they committed was downright Rape ... these new-fashion'd thieves seiz'd upon her, took her Prisoner, toss'd her in a Blanket, ravish'd her, and in short us'd her barbarously, and had almost murther'd her

Much of the political and public rhetoric in recent years has been focused on criticism of financiers (but, unlike Defoe, not before 2006). However, given the performance of Europe's politicians since 2008 is terrifying (for a European citizen) in that they seem to refuse to take responsibility (which countries were the first to break Euro rule, was it Germany and France?) and prefer to see the crisis as an opportunity to score political points (the Conservative party in the UK).

The British, between around 1688 and 1728, seem to have recognised the democratic nature of markets. Something that Aristotle commented on, and was discussed by scholastics that influenced the development of science through the likes of Bradwardine and Oresme. Napoleon was scornful as Britain as a nation of shopkeepers, but that is precisely where its strength lay. And it is not simply a financial strength, how different is Defoe's description of a Tradesman from Hume's empiricism?

Nature, the British version of Science, rarely makes forays into exploring issues in finance. They invited me to talk at a meeting in September 2009 and I get the sense that they would like to do more but are a bit perplexed by the subtleties of finance. The mind is willing but the body is weak.

In October 2008 Nature published a piece, Economics needs a scientific revolution, by the French econo-pysicist Jean-Philippe Bouchaud, which argued that the fault was with the academic discipline of economics: "Classical economics is built on very strong assumptions that quickly become axioms" where as "Physicists, on the other hand, have learned to be suspicious of axioms. If empirical observation is incompatible with a model, the model must be trashed or amended". More recently they have published a broader article, reflecting the diffusion of the financial crisis into society at large, Science's attitudes mustreflect a world in crisis, by the science writer Colin Macilwain.

Physicists are never slow to criticise the short-comings of other disciplines, but the truth is physics, with its never changing laws, is simple. While physicists are paddling in the play pool, economists are hanging on to a rubber ring in the middle of a North Atlantic gale. It is not surprising they don't look like good swimmers. That said, economists are well aware of the limitations of their discipline. From the mathematician Cournot's criticism of the economists' use of mathematics in the 1830s to the contemporary economist's criticism of the wholesale adoption of the ergodic hypothesis by Paul Davidson, economics could do better.

Since the Second World War, economics has transformed itself from a relatively minor discipline to a dominant field. It is ironic that in the 2008 "Research Assessment Exercise", UK economists judged their work to be "excellent", just as the tsunami of the credit crisis was crashing on the shore. This dominance was built, substantially, on "positive" economics, adopting the ideals of the logical positivists that emerged in central European maths and physics in the aftermaths of the First World War. The authority that these scientist had rested on the fact that they had defeated Germany and Japan.

It was not square-jawed commandos that defeated the Axis, but mathematicians and physicists (like Turing, von Neumann, Kolmogorov, Weiner, Shannon, ... the list is not short) working in Operations Research, the Manhattan Project and code-breaking, that won the war. In particular the code breakers were able to transform streams of random letters into meaningful messages. This analogue seems to have driven economic research through the fifties and sixties: given the right algorithm the randomness of asset prices can be read. Then, just as the idealised economic order of Bretton Woods collapsed under the reality of people and politics, Black-Scholes-Merton and financial mathematics (apparently) emerged to save the world from random chaos.

The financial crisis of 2007-2009 was a demonstration of limitations of the science that emerged out of logical-positivism and in particular the ergodic hypothesis placed at the core of positive economics. It was not a failure of maths and science in general, but a particular type of science that emerged in the 1920s and dominated society between 1940 and the present.

Macilwain is concerned with he fact that many science policy gurus, generally wedded to the tenets of positivism, are "clearly more comfortable discussing the planet's ecological crises than the economic ones currently alarming the general population" and that there is "great danger is that scarce funding will consolidate around single-discipline research". More Big Physics like the LHC, or repeating Tony Blair's "betting the house"on genetics - a bet that has not paid out.

Financial markets are manifestations of random, non-ergodic phenomena, as such they can hardly be amenable to deterministic techniques. Specifically, a single approach to understanding them, whether rooted in analogues from the Olympian disciplines of mathematics, physics or biology, will fail. Scientific revolutions have historically been based on the inter-disciplinary interaction, such as between financiers, lawyers (Bacon, Descartes, Fermat, Huygens) and mathematicians. If society stops to think about the current financial turmoil and what it can tell us, we would surely be at the dawn of another scientific revolution.

Friday, 4 November 2011

It is well known that Leonardo Da Vinci became interested in the "golden ratio" or "divine proportion". It is somewhat less well known is he learnt about the number from Lucca Pacioli, the Francisican friar and grandfather of accounting. What is virtually unknown is that Pacioli probably learnt his mathematics from the financial mathematician and artist, Piero della Francesca (as an artist).

I have written an article, Decoding Da Vinci: Finance, functions and art, on this for plus! an on-line magazine aimed at youngster. The piece explains why the ratio was considered divine because of its form as a continued fraction, and how another financial mathematician laid the foundations for functional analysis by popularising decimal notation.

Tuesday, 4 October 2011

On April 16 2010, the SEC filed fraud charges against Goldman Sachs, the “great vampire squid wrapped around the face of humanity”. The case in court is that the bank claimed the assets in the fund ABACUS 2007-AC1 were selected by an independent advisor, when in fact they were selected by John Paulson to enable his funds to short the assets, and in making the claim, the bank deceived investors. However the case is usually presented as the bank being taken to court for acting immorally structuring an asset designed to fail and selling this on to unsuspecting clients (for example The New York Times’ report and their prediction in December 2009 or in the UK Jeremy Warner of The Telegraph). The vampire squid was sucking the life out of innocent investors.

The SEC could not take Goldman Sachs to court for acting unethically, the courts are about legality not morality. However, it would come as a surprise to many that, according to Catholic doctrine at least, there was probably not much morally wrong with Goldman’s actions.

In the third quarter of the thirteenth century, Thomas Aquinas worked on his SummaTheologica, integrating Aristotelian philosophy with Catholic doctrine and established himself as a “Doctor of the Church”. In the “Second part of the Second part” of the Summa, Aquinas addressed the issue of individual morality, including the concept of justice. One question the theologian considered was “Whether it is lawful to sell something for more than it is worth?” and examined a case presented by Stoic philosophers

A grain merchant from Alexandria arrives at Rhodes, which is gripped by famine. The merchant knows that other merchants are following him with plentiful supplies of grain, though the town’s inhabitants do not know this. How should the merchant price the grain he has? ( De Officiis Book 1, XII)

The Roman jurist Cicero (Tully) was typical in arguing that the merchant should not take advantage of the misfortune of the starving and charge a lower price based on the knowledge of the coming relief.

Aquinas disagrees

in the case cited, the goods are expected to be of less value at a future time, on account of the arrival of other merchants, which was not foreseen by the buyers. Wherefore the seller, since he sells his goods at the price actually offered him, does not seem to act contrary to justice through not stating what is going to happen. If however he were to do so, or if he lowered his price, it would be exceedingly virtuous on his part: although he does not seem to be bound to do this as a debt of justice. (Summa II.II Q77(A3) Reply to Obj. 4)

This is an almost shocking conclusion from a saint. To Aquinas, the merchant, having arrived at Rhodes, may think there are more grain shipments on the way, but does not know. Aquinas argues that

because the just price of things is not fixed with mathematical precision, but depends on a kind of estimate, so that a slight addition or subtraction would not seem to destroy the equality of justice. (Summa II.II Q77(A1) Reply to Obj 1, para 2)

It is not unjust to charge the higher price, since whether of not this price is ‘just’, or not, is uncertain.

Aquinas’ concept of the “equality of justice” comes from Book 5 of Aristotle’s NicomacheanEthics which had been translated into Latin in 1250. In Ethics, Aristotle considered the morality of economic exchange and argues that market exchange is not performed in order to generate a profit, for gain, but to correct for inequalities and to establish a social equilibrium. Using the example of a builder and a shoemaker, Aristotle argues that

The builder, then, must get from the shoemaker the latter’s work, and must himself give him in return his own. (Ethics p 79)

For justice to exist in the exchange, there needed to be an equality between the shoes the shoemaker produced and the results of the builders’ work. For such an equality to exist, there needed to be a measure of the value of the goods produced by the builder and the shoemaker to enable a just exchange . This measure, the price, was provided by money.

all things that are exchanged must somehow be comparable. It is for this end that money has been introduced, and it becomes in a sense an intermediate; for it measures all things. (Ethics p 79)

The relationship at the heart of the exchange between the shoemaker and the builder that Aristotle went on to establish was explained mathematically, as a geometric relationship. This was significant since Aristotle never used mathematics in addressing questions in physics.

However Aquinas’ use of an analogy with mathematics was not simply following Aristotle, he was re-interpreting in the context of contemporary events. The twelfth century had seen a “renaissance” in western Europe, a population explosion that brought with it Gothic architecture and a commercial revolution.

In the aftermath of the collapse of the Roman Empire in the west, the concept ofturpe lucrum, or ‘shameful gain’ emerged and merchants were restricted in what prices they could charge. As Europe emerged out of the ‘castellan’ society, characterised by isolated local lords held together by feudal service relations, into one of integrated trade networks, turpe lucrumwas no longer a feasible basis on which to run the economy. It was in this environment that Leonardo of Pisa, Fibonacci, published the Liber Abaci.

One aspect of the complexity of the transactions was to disguise usurious contracts. There is a subtle difference between usury, which is associated with charging for the use of money, and interest which is a compensation for loss. For example a farmer could lend a cow for a year and expect to be re-paid with a cow and a calf, since in the normal course of events a cow would give birth to a calf over the year. Interest could be charged on ‘productive’ assets, with the consequence that all, legitimate, medieval securities would be ‘asset backed’. Gold, being inorganic, was not productive and so charging for its use was unjust.

However, this attitude to money stifled innovation and so more complex structures emerged to disguise the charging of interest on a money loan. For example, the ‘triple contract’ enabled an entrepreneur to raise money to invest in a trading venture. At the heart of the triple contract was a partnership between the entrepreneur and investors, this was the first contract. The second contract would be an insurance contract taken out by the entrepreneur to insure against the loss the investors’ capital. The third contract was another ‘insurance’ contract given to the investors by the entrepreneur, where by the investors surrendered their rights to a share of the profit in exchanged for a fixed payment from the entrepreneur, this payment was guaranteed by the second contract. Not quite a Credit Default Swap but definitely credit insurance.

Eventually, in 1236, the canon (church) jurist, Alanus Anglicus, determined that turpe lucrum did not exist if the future price of the good was uncertain in the mind of the merchant and this ruling was embedded in Catholic doctrine some ten years later. Aquinas, in the Summawas integrating the theories of the newly translated Aristotle with emerging Catholic doctrine and existing commercial practice to argue that a profit was ‘just’ so long as it was uncertain and might lead to a loss, it entailed a ‘risk’.

Islamic societies had equally stringent prohibitions on usury, and so this alone cannot explain why Fibonacci would have such an influence in Europe. The key difference between the environment for medieval European merchants and their colleagues in the Middle East, India or China was the range of currencies being used, a consequence of the castellan society of the ‘Dark Ages’. For example there were 28 different currencies in Italy at one time or another and as Groetzman has observed

Reading Liber Abacione has the sense that Italian merchants of the 13th century operated in a world of complete relativism. With no central government, no dominant currency, and even competing faiths and heresies, value is expressed quite abstractly only in a set of relative relations to other items. (NBER Working Paper No. 10352, 2004)

It was in this environment that ‘arbitrage’, the process by which one commodity ‘arbitrates’ between the value of two other commodities, just as money ‘mediates’ between the value of two commodities, emerges and is discussed in the Liber.

Aristotle’s use of mathematics in examining the nature of exchange was first noted by the medieval proto-scientist, and Aquinas’ teacher, Albert the Great. This observation was important philosophically since it separated the measure from the measured, money does not share the same ‘nature’ as shoes. This seems insignificant today, but at the time it was an important conceptual development that spawned a ‘mania’ for measuring and mathematics such as that undertaken by the ‘Merton Calculators’.

The historian Joel Kaye has argued that the line of thought initiated by Albert and Aquinas developed by Oresme and the Calculators, was based on

the transformation of the conceptual model of the natural world ,…, [which] was strongly influenced by the rapid monetisation of European society taking place [between 1260–1380] (Kaye, p 1)

The scholars took their approach to nature having observed the operation of the markets that had emerged in the century before and in response

[were] more intent on examining how the system of exchange actually functioned than how it ought to function. (Kaye, pp 219-220)

Kaye, and a fellow historian, Alfred Crosby, believe this paradigm shift played a pivotal role in the development of European science. The process of this conceptual change is clear. Innovations in finance led to the development of vernacular mathematics encapsulated in theLiber Abaci and disseminated through abbaco schools. University based scholars then began to try and make sense of what was actually happening and tried to identify the essence of the markets, with Aquinas concluding that a profit was ‘fair’ provided that it was uncertain and came with the risk of a loss. In modern terms, a market was viable if it did not admit arbitrages, so long as there is ‘No free lunch with vanishing risk’.

In much of the public discourse on modern finance, financial institutions are presented as immoral and rapacious beasts, initiating ‘unnatural’ financial instruments in order to take advantage of the innocent. These opinions belie a more complex reality, that finance is integral to society, complex financial products have been with us for at least 900 years, that when people, like Aquinas, employ reason and morality to examine the markets there are some surprising conclusions, and that the study of markets leads to profound insights for science in general. Criticism of finance is as likely to reflect a lack of rationality and morality in society, in general, than a specific lack of ethics and reason, in the markets.

Wednesday, 21 September 2011

Scott Patterson, in his book The Quants, describes Ed Thorp as the 'godfather' of Quants. Without doubt, Thorp heralded the modern age of quantitative finance, but does this mean he was the first Quant?

Many might point to Louis Bachelier as being the original Quant. Bachelier had been born in Le Harve, in Normandy, in 1870. His father was a wine-dealer while his mother came from a banking family. In the six months after graduating from school, both of Bachelier's parents died and he was forced to take over the management of the family firm, Bachelier fils, to provide for his younger siblings. After doing his military service in 1891, Bachelier moved to Paris and became involved in the Paris Stock Exchange. Simultaneously, he enrolled on the mathematics degree at the University of Sorbonne, where Poincare was a professor. He was not a brilliant student but in 1895 he embarked on a doctorate that synthesised the activities being undertaken at the Paris Stock Exchange and the theories of heat and of probability, at the cutting edge of physics at the time. Bachelier then left finance and embarked on an academic career that lasted the following forty years, a career that appears to have been hindered by his early association with the markets.

This, however, is not the career path of a Quant. The likes of Ed Thorp and James Simons had a training in science that they then applied to finance, Bachelier had started working in finance and used this experience as the basis of an academic career: he was a 'reverse-quant'.

The history of reverse-quants is probably more significant than that of Quants. Leonardo Bonacci, better known as Fibonacci, could claim to be the first reverse-quant, taking ideas from contemporary finance to change European culture, by changing not just how merchants undertook their business calculations, but how western science wrote mathematics.

Leonardo's father, Guglielmo Bonacci, was a merchant looking after the Pisan interests in the Algerian port of Bejaia. While we might not imagine that medieval finance was very sophisticated, we would be wrong. The historian Alfred Crosby describes a series of transactions undertaken by an Italian merchant, Datini, which, although they took place two hundred years later, would have been similar to the types of transactions Guglielmo Bonacci would have been involved in. In November 1394 Datini bought wool forward from Mallorca. The wool was sent to Pisa, via Barcelona, in summer 1395, arriving in Italy the following January. Datini sold some wool to a colleague in Florence and processed the the rest into cloth, which he sent to Venice for shipping back to Mallorca for sale in July 1396. However the market in the Balearics was weak and so the cloth was transported to Valencia and North Africa. The last piece of cloth was sold three and a half years after the wool was originally been contracted from the shepherds. Datini would have engaged in forward contracts, loan agreements and transactions in at least five currencies (Arogonese, Pisan, Florentine, Venetian, North African). To make a profit, he needed to be an expert at 'commercial arithmetic', or financial mathematics.

Fibonacci was born in Pisa around 1170 and educated, not only in Bejaia but, as far afield as, Egypt, Syria, Constantinople and Provence. He would write a number of books on mathematics, but his first and most influential was the Liber Abaci('Book of Calculation'), which appeared in 1202. The Liberwas heavily influenced by the Arabic book 'The Comprehensive Book on Calculation by Completion and Balancing' written around 825 CE by al-Khwarizmi, who was himself motivated to write the book because

and his book provided the easiest way of arriving at that number, using al-gabr ('restoration') and al-muqabala('balancing'). Fibonacci collated these Arabic techniques into a single textbook for merchants, such as Datini, facing the increasingly complex financial instruments and transactions emerging at the time.

The impact of the Liber Abaci was enormous. Fibonacci became an adviser to the most powerful monarch of the time, Frederick II, Holy Roman Emperor and King of Sicily. More significant, Abaco or rekoning schools sprang up throughout Europe teaching apprentice merchants how to perform the various complex calculations needed to conduct their business. Pacioli, who taught Leonardo da Vinci maths, was a well known graduate. Less well known is the fact that Copernicus came from a merchant family and in 1526, seventeen years before his more famous, "epoch-making" 'On the Revolutions of the Heavenly Spheres', he wrote 'On the Minting of Coin' about finance.

The practical usefulness of the reckoning schools was that, by using positional numbers and algebra, merchants could execute complex financial calculations that would typically include an illicit interest charge, hidden from the mathematically unsophisticated, university based, Church scholars. The merchant bankers were using mathematics to keep one step ahead of the regulator and the effectiveness of the non-university mathematics would not have been lost on the sharper scholastics, observing market practice.

The most influential single Abacograduate has to be the Dutchman, Simon Stevin. Stevin, who was born in 1548 in Bruges, had originally worked as a merchant's clerk in Antwerp then as a tax official back back in Bruges, where he wrote his first book Tafelen van Interest('Tables of interest') which he published in 1582, before moving to the University of Leiden in 1583. About this time, he was appointed as adviser to Prince Mauritz of Nassau, who was leading the Dutch revolt against the Spanish, and eventually became the Dutch Republic's Finance Minister.

As well as being active in government, Stevin carried out scientific experiments, and it is believed his bookeeping inspired his physics. His most famous experiment showed that heavy and light objects fell to the earth, in the absence of air resistance, at the same speed, an experiment that disproved a belief of Aristotle and is usually attributed to Galileo dropping things from the Tower at Pisa some years later.
One of Stevin's most important posts was as the director of the Dutch Mathematical School, established in 1600 by Mauritz to train military engineers. In this capacity, in 1605, he published a textbook for the School, the 'Mathematical Tradition', which was a comprehensive overview of mathematics and included a whole section on 'Accounting for Princes in the Italian manner'. In a very short period, the Dutch Mathematical School became the centre for merchants' training in north western Europe. This success, in turn, forced the authorities at the University of Leiden, which provided the School with its facilities, to take practical sciences, in particular maths, a bit more seriously. The Dutch Mathematical School would inspire the soldier Descartes to study maths and would train Huygens and a whole generation of European scientists. In addition, it was Stevin's promotion of the use of decimals, to aid accounting, that inspired Newton to think of functions as power-series, giving birth to the discipline of Analysis.

So much for 'reverse-quants'. If a Quant is defined as a someone who moves from an academic career into finance, the most famous Quant is Isaac Newton. Newton essentially finished his work in physics with the publication of Principia in 1687, his last significant work, Optiks, published in English in 1704, was based substantially on research undertaken in the early 1670s. After almost a decade of troubles, Newton moved into finance in April 1696 when he was appointed Warden of the Royal Mint. This was a largely ceremonial post, but Newton took to it so much that he became the Mint's operational manager, its Master, in 1699 (see Isaac Newton: Financial Regulator).

Being Master gave Newton an average income some 16 times what he would have had as an academic. Today a 'starting' salary for a jobbing professor in England is around £60,000, and we could expect the Lucasian Professor at Cambridge to earn somewhat more than this. On this basis, the equivalent salary for Newton as Master of the Mint is in excess of £1 million, which pretty well places him in the bulge bracket. Newton, no longer needing the income from his position in Cambridge, resigned his Professorship at the end of 1701. Newton did become President of the Royal Society in 1703, an institution whose foundations were laid by the banker Thomas Gresham, and Newton followed in the footsteps of his patron, the the English Chancellor of the Exchequer, Charles Montagu. Gresham and Montagu, central to the establishment of the oldest national academy of sciences, are just two more examples of 'reverse-quants'.

Newton might be the most famous Quant, but he was not unique or the first. Huygens identified conditional expectation while investigating the pricing of life annuities, and J. Bernoulli identified the number ewhen investigating interest payments. Generations before Huygens, Bernoulli and Newton, we have Galileo, who was born in Pisa around 1564. He was appointed to the Professorship of Mathematics the prestigious University of Padua in 1592, where he made his famous astronomical observations. Galileo had been short of money all his adult life, as a mathematician he was poorly paid and was expected to supplement his salary by taking private students, but this interfered with his research. In 1613 the Duke of Tuscany, Cosimo II de Medici, offered Galileo the position of 'First and Extraordinary Mathematician of the University of Pisa and Mathematician to his Serenest Highness (i.e. Cosimio)' with a large salary and no duties, an ideal post for Galileo. It was some time in the next decade or so that Galileo wrote 'Upon the Discoveries of Dice', which he was almost certainly asked to write by Cosimo, who may have been trying to solve a practical problem in gambling. Galileo did not leave Padua to work in finance, but he did become the mathematical adviser to the the head of one of Italy's most important banking families. Ironically, had Galileo stayed at Padua, under the protection of the religiously ambivalent Venetians, he would never had faced the Inquisition, and possibly would not have become as famous as he is today.

European science did not start in the Renaissance, it existed in the High Middle Ages. The 'renaissance' of the 'long twelfth century' resulted in what the historian Joel Kaye describes as

the transformation of the conceptual model of the natural world ,..., [which] was strongly influenced by the rapid monetisation of European society taking place [between 1260-1380].

and played a pivotal role in the development of European science. Thirteenth century scholars

[were] more intent on examining how the system of exchange actually functioned than how it ought to function..

It seems that Fibonacci did not just influence medieval merchants, those scholars keeping an eye on merchant's dubious dealings, also, became obsessed with mathematics. This included the great scholastic scientist, Albert the Great, and the mathematically minded theologian, Thomas Aquinas. But the most famous scholars to turn to mathematics were the 'Merton Calculators'.

The first of the Calculators was Thomas Bradwardine, who entered Merton College in Oxford in 1323. While studying the quadrivium, mathematics, astronomy, music and geometry, Bradwardine observed that

[Mathematics] is the revealer of genuine truth, for it knows every hidden secret and bears the key to every subtlety of letters. Whoever, then, has the effrontery to pursue physics while neglecting mathematics should know from the start that he will never make his entry through the portals of wisdom.

This was a highly significant point in the history of science since it is the first time that scholars in the Hellenistic tradition, which included Jewish, Christian and Islamic philosophers, innovated in physics by using mathematics. In the footsteps of Bradwardine there was, amongst others, William Heytesbury, who identified the mean speed theorem, and Nicolas Oresme, who introduced the idea of the graph and advised the French king on money supply.

After twelve years at Merton, Bradwardine left the Oxford University to work for the Bishop of Durham, who was the Treasurer and Chancellor of England. So Bradwardine was not only the first Physicist, as we would understand the term today, he was also the first person who left an academic career to take up one in finance. The first Quant was the first Physicist.

Looking at the relationship between scientists and finance reveals some important facts. Firstly, the migration from academic careers in science to finance appear to be embedded, it is not a modern phenomena. However, possibly more significant is the less well-appreciated role of the 'reverse-quants' in the development of science. The influence is captured by events in France in 1304-1305 when economic instability and a market failure led the French King, Philip the Fair, to issue decrees fixing the price of bread. His decrees failed spectacularly, and this was seen by contemporary observers as evidence that 'nature' ruled, and not the authority of the King, and that market prices where an objective, 'scientific' measure. This enabled the likes of Bradwardine to re-assess the role of mathematics in science. Later, people trained in commercial arithmetic - financial mathematics - such as Copernicus and Stevin, were able to challenge the authority of Aristotelian science, and argue that the Earth revolved around the Sun and that heavy and light objects fall at the same speed. Today, financial markets challenge assumptions about determinism and stability of systems, the question is, can science meet those challenges?

Could mathematicians have done more to ensure that their models weren't abused, or is it not really about maths at all?

Jack's deceptively simple question is incredibly intricate. There are many commentators who argue that the complexity of modern markets is such that they are mathematically intractable, and the best approach is analysis through discourse, as was popular in the Dark Ages and between the Black Death and Francis Bacon and Galileo. My (biased) opinion is that these views are held principally by those educated in the ethos that developed before the collapse of Bretton-Woods, when a deterministic economy was managed by wise sages. Unfortunately the world is not deterministic and the sages could not hope to manage the economy by agreeing treaties in luxury hotels.

However, mathematics itself cannot present a unified front. We have Paul Wilmott and Nicolas Nassim Taleb arguing that the mathematical techniques that dominate the markets today, that of Ioannis Karatzas, Steven Shreve, Mark Davis (whom Wilmott has famously libelled in an ad hominen attack) and a Marek Musiela, to name a few, is the wrong sort of mathematics. This is rather like someone claiming a Toyota Prius is not really a car in comparison to a Dodge Pickup, the fact that the Prius is unfamiliar does not mean it is not technically superior.

However, this does not mean that the academic discipline of financial mathematics does not have some issues to address. The publication of the Heath-Jarrow-Morton framework created a demand for stochastic analysis skills in the markets, displacing the skills in the numerical solution of deterministic differential equations familiar to Wilmott, Taleb, physics and engineering. This demand was met by the universities with a plethora of Financial Mathematics Masters degrees. I feel that now the markets have moved on, but whether many of the MScs are keeping up, I am not so sure.

Part of the problem is that many academic mathematicians are more comfortable walking across campus to chat to their colleagues in the economics or finance departments than talk to mathematicians with direct experience of the markets, such as Claude Shannon, Edward Thorp and James Simons. This means that the orthodoxy of Samuelson and his progeny dominates and ideas such as the Kelly Criterion, and those of stochastic control familiar to electrical engineering, have been missing from the rarefied curricula of some financial maths degrees.

But all this is a discussion of plumbing of the markets, a utility, and mathematics is not really a utility. Mathematics is a science.

For Laplace, the roll of a dice is not random, given precise information of the position, orientation and velocity of a dice when it left a cup, the result of the roll was perfectly predictable. At the heart of Laplace's determinism was knowledge, and `probability' was a measure of ignorance, and not of 'chance'. As a product of the Enlightenment, Bernoulli's God is replaced by 'an intellect', Laplace's demon. The positions of Laplace and Bernoulli, however, differ significantly from Cicero who, in De Divinatione, distinguished between the predictable (eclipses), the foreseeable (the weather) and the random (finding of a treasure). But between the Bernoulli's religious and Laplace's atheist conceptions of predestination, there is more than just a change in wording; there is a huge philosophical divide that was one of the key achievements of the Enlightenment.

A persistent problem with determinism is that it, logically, can lead to a collapse in moral responsibility. The syllogistic argument is:
Premise 1. Actions are either pre-determined or random.Premise 2 If an action is pre-determined, the entity who performed the action is not morally responsible. Premise 3. If an action is random, the entity that performed the action is not morally responsible. Conclusion. No one is morally responsible for their actions.

An achievement of the Enlightenment was to realise that moral responsibility should not sit in the conclusion, but as a premise, and the argument became.Premise 1. People should be held morally responsible for their actions. Premise 2. If someone (i.e. a child) cannot foresee the consequences of their actions they cannot be held morally responsible for their actions.
Conclusion. Moral responsibility requires that there be foresight.

In order to be 'morally responsible', people needed to have a degree of foresight, which can only be obtained through knowledge, or science. This is the fundamental purpose of science, to enable people to take responsibility for their actions, whether related to the safety of industry or personal diet. This was reflected in Humboldt's view that education should turn 'children into people', but very different from Bacon's opinion that 'knowledge is power'.

Society needs science to interact with the markets because science creates knowledge, knowledge enables foresight and foresight leads to responsibility. If there is no science of finance, there can be no responsibility in the markets (if the Enlightenment was right).

Poincare dismissed the idea of 'science for science's sake', science is not a recreational pursuit. Scientists need to ask the difficult questions at the extremities of knowledge and mathematics role is to tackle the questions that cannot be answered by experimentation. This is why the the $3 billon investment in the Large Hadron Collider, in looking for the Higgs Boson, is seeking to prove a mathematical derivation. Physical sciences are impotent in reaching out to the boundaries of knowledge without mathematics clearing the path.

The financial markets cannot be experimented on. The very fact that they are complex means that the only tool science has in trying to understand them is mathematics. The fact that the, predominantly, deterministic mathematics based on physical phenomena that most people are familiar with (even frequentist or objective probability is rooted in the 'physical' act of counting) is insufficient to understand the markets does not mean that mathematics will not provide the key to understanding the markets. The point is, it will be "mathematics, but not as we know it", it needs to be created.

If society wants to understand the markets, and really wants them to act responsibility, it needs to fund financial mathematics on a par with the investment made into the physically very small or the very distant.

Robert Peston, the BBC’s Business Editor who broke the news of the Credit Crisis to the British public in 2007, has said that in the months leading up to the crisis he had tried to report on Collatorallized Debt Obligations but had not been able to find a banker who could explain them to him (seeWhat is Financial Journalism for? Ethics and Responsibility in a time of Crisis and Change p 20). This point gets to the crux of the Credit Crisis, “no one” saw it coming and the responses of the US and UK governments was inadequate because there had been no public discussion of developments in finance, as there are of developments in, for example, energy, nano or genetic technologies. The result was society was completely unprepared for what would unfold in 2007-2008.

In writing An Engine not a Camera Donald MacKenzie, a sociologist working in ‘Science and Technology Studies’, hopes that there will be “richer conversations” about financial markets, and out of these discussions a better, and stronger, financial system will emerge. Science and Technology Studies examines how social factors affect technological progress and one of its pioneers was Robert K. Merton, father of one Robert C. Merton. While STS is not popular amongst many physical scientists who like to believe their knowledge is based on indisputable fact, there are numerous financial mathematicians who, following Poincaré (see The Value of Scienceespecially Science and Hypothesis) , see facts in the context of theory, which is constructed in a social context.

The central thesis presented by MacKenzie is that modern financial markets ‘perform’ financial theory. That is, finance practioners have been trained by universities to believe a set of cohesive ideas which they then, on graduation, employ in the markets. Since the ideas are the same, whether presented in Europe or in salt-water or fresh-water universities in the US, the heterogeneity of countless individual agents is replaced by a single Homo economicus. The immediate consequence of this is the commoditisation of finance theory; models are ‘shrink wrapped’ and become ‘black boxes’ with the subtleties of their underlying assumptions are irrelevant. The more dramatic result is that, eventually, the ‘performed’ markets become so far removed from the reality of finance that that they collapse in an episode of ‘counter-performativity’. MacKenzie describes in detail two examples of what he sees as counter-perfomativity, Black Monday in 1987 and the failure of Long Term Capital Management eleven years later.

In support of this hypothesis MacKenzie discusses in detail how modern derivative markets emerged and how, alongside the evolving markets, modern finance theory was created. His history of the development of finance theory, between 1950 and the 1990s is possibly unrivalled being based on extensive interviews with pretty much everyone who has made a significant contribution, including Markowitz, Samuelson , Friedman, Merton, Scholes, and Harrison. Underpinning these narratives is a discussion of the relationship between the ‘practice’ of finance and the academic theory, and it is in this context that MacKenzie offers an explanation why Black-Scholes-Merton received the Nobel Prize while Thorp and Kassouf have been generally ignored in the university classroom.

While a reader may have an issue with MacKenzie’s core hypothesis, his account of how finance has developed makes the book is essential reading for anyone who is seriously interested in modern financial theory.

The book’s weakness is that it was written in the aftermath of the failure of LTCM, a time when the importance of the martingale approach to derivative pricing was only beginning to be understood. While the text does discuss the work of Harrison, Kreps and Pliska it does not go on to discuss the importance of the ‘Fundamental Theorem’ (that a market is arbitrage free if a risk neutral pricing measure exists, and complete if the measure is unique). Ironically for sociologists, the Fundamental Theorem is based on Black and Scholes's observation that it should not be possible to make a risk-less profit, which is almost a statement of commercial morality and so is socially constructed.

The strength of the book is that it highlights the dangers of adopting financial models as black-boxes rather than crafting solutions relevant to specific situations. This is highlighted in his analysis of the failure of LTCM, where MacKenzie rejects many of the popular explanations for the fund’s failure, making the observation that criticising hedge funds for taking on risk is rather like criticising aeroplanes for leaving the ground. While the events of 1998 may seem irrelevant in the aftermath of 2007, MacKenzie has undertaken a similarly comprehensive review of the Credit Crisis in the context of performativity and counter-performativity. Again the message he delivers is to employ fundamental skills that can question the received wisdom of the dominant models, a message that finance would do well to heed.

Friday, 12 August 2011

Alongside the stock market boom of the 1690s was rampant inflation, caused by the fact that much of the coin circulating in England had been clipped and there was widespread counterfeiting. The inflation came about because, at the time, silver was an absolute measure of price. If English coins lost silver, more were needed to pay the foreigners, and so the importers would ask for more coin from their domestic customers. [Craig, 1946, p 8]

This, physical, process was compounded by the growth in banks’ lending, increasing the supply of money chasing, pretty much, the same volume of goods, further depressing the value of money. The result was a collapse of confidence in the value of the coin that the English government was using to pay its debts. In 1696 the government decided that confidence would be restored only if the Royal Mint replaced all the silver coin in circulation with sound coin.

Almost simultaneously, and apparently not by design, Newton was appointed Warden of the Royal Mint in April 1696. While the publication of Principiahad made little impact during the last days of James II Stewart’s reign, when William III took up residence at Hampton Court, Christiaan Huygens, whose elder brother Constantijn Huygens was an adviser to William, introduced Newton to the new court. Another of William’s advisers was the English Puritan philosopher, John Locke, who had been a political exile in the United Provinces since 1683. Locke and Newton became firm friends and Locke took it upon himself to secure a lucrative post for Newton, who seems to have become bored with Cambridge after exposure the excitement around William’s court, filled with soldiers, statesmen, bankers and scientists [Levenson, 2009, p 44–46].

The period 1690–1695 proved difficult for Newton, his work gravitated to theology and he developed an intense relationship with a young Swiss man, Nicolas Fatio de Duiller, which ended in 1693 and shortly after Newton appears to have had a nervous breakdown (He had had one in 1678 also) . In the aftermath, Locke and the President of the Royal Society, who also happened to be the Chancellor of the Exchequer, pulled strings and secured the Wardenship for Newton.

While Newton, along with everyone else, had been asked to give his opinion on what to do about the coinage, it seems the initial appointment was more ceremonial than practical. The Warden was the monarch’s representative at the Mint and had historically been the most important post there until the crown stopped charging seiniorage, a fee for minting coins, in 1666. After that point the Master, the manager of the mint, became its most important, and best paid, employee [Craig, 1946, p 1–4].

The re-coining, by emptying the economy of coins, precipitated what has been described as “the gravest economic crisis of the century” [Murphy, 2009, p 56], a century that included the devastation of the Civil War, the stop on the Exchequer and the boom and bust of the infant stock market. The government were not happy and, in time honoured fashion, pointed the finger at the Mint’s operations rather than blame their own policies.

Newton, as Warden, was called in front of the Parliamentary Committee on Mint Miscarriages in 1696. One of the witnesses for the prosecution, appearing in 1697, was William Challoner who proposed a series of improvements for the Mint, which Newton dismissed. The Committee of politicians preferred the advice of Challoner over that of the physicist and so Newton responded to this turn of events ‘rationally’, by locking Challoner in Newgate prison. Newton, as Warden could do this, but had to release Challoner after seven weeks, at which time Challoner, as might be expected, stirred up a hell of a row.

Around a year after Challoner’s first appearance in front of the Committee, Newton was called before it to justify his his treatment of the man. Newton had spent the intervening year, and £910s, investigating Challoner. It turns out that Challoner had started out as a labourer but through counterfeiting, theft, fraud and duplicity, become a wealthy gentleman. His whole ploy, it seems, had been to get appointed to the Mint, to support his criminal activities. Challoner was executed in March 1699 following a prosecution managed by Newton, who was ‘promoted’ to Master of the Mint at the end of the year [Craig, 1946, p 17–19].

Being Master gave Newton an average income some 16 times what he would have had as an academic. Today an ‘average’ salary for a jobbing professor is around £60,000, and we could expect the Lucasian Professor at Cambridge to earn somewhat more than this. On this basis, the equivalent salary for Newton as Master of the Mint is in excess of £1 million [Levenson, 2009, p 239]. Newton no longer needed the security of his position in Cambridge and he resigned his Professorship at the end of 1701.

Newton is often presented as being difficult to get along with, for example a positive assessment published by the Royal Society in 1995 gives the following summary

Isaac Newton was a humourless, solitary, anxious, insecure and private man with obsessional traits. He was poor at human relationship, such as the expression of gratitude [Keynes, 1995]

However this picture is at odds with the picture painted by Sir John Craig, who wrote about Newton’s work at the mint in Newton at the Mint in 1946,

Newton appears to have been a good judge and handler of men, and he had some magnetism which in many engendered an extraordinary regard and respect [Craig, 1946, p 119]

and “He had the tact to allow for political or human aspects”. Moreover,

he was a good bureaucrat, he insisted on the preservation of clear and exact records …[he had] care and restraint in considering new outlays of public money, with indifference to waste or extravagance that had become customary [Craig, 1946, p 120]

Craig's views are supported by the fact that John Maynard Keynes described Newton as “one of the greatest and most efficient of our civil servants,” no small praise from the man who managed Britain’s finances during the First World War.

Newton’s more anti-social behaviour is attributed to insecurity originating in Newton’s difficult childhood, an insecurity that seems to have remained with him throughout his time in science. However, Newton seems to have taken to his role at the Mint like a duck to water, and maybe being able to see the broader relevance of his intelect to the wealth of the nation, gave Newton the confidence to start enjoying life.

Newton did not completely abandon science, he became President of the Royal Society in 1703, holding the post until his death, but his last significant work, Optiks, published in English in 1704, was based substantially on research undertaken in the early 1670s. However, Newton played an active role in finance for the rest of his life. One of his most significant acts was in setting the exchange rate between gold and silver in 1717, an exchange rate that would shift Britain from the silver standard to the gold standard.

English money had always been associated with silver, giving us the term ‘sterling silver’, this was in common with much of Europe, India and China but different from the Middle East, who based money on gold. By 1710 Britain was running short of silver coin because the amount of silver in a coin was making it worthwhile to convert coin into dinner services. Newton’s solution was to reduce the amount of silver in a coin, a pound of silver should be used to make 64.5 shillings instead of 62 shillings. This was not popular with the government, as it was seen as devaluing the coin, and so would result in inflation. Therefore Newton, according to Craig,

translated the conclusion into the mathematically equivalent but impractical proposition that silver coin should retain its weight and be left to rise in value by force of scarcity [Craig, 1946, p 107].

This situation continued until in 1717 the government saw the solution as increasing the value of the Britain’s main gold coin. On Saturday 21 December 1717 the government asked Newton to fix the sterling silver exchange rate with the main gold coins used throughout Europe, in a report ‘blinding with science’ [Craig, 1946, p 108], the value of the British gold guinea increased from being worth only 20s of silver, to being worth 21s. The Law of Unintended Consequences kicked in, Newton had undervalued foreign gold coins. The result was described by Adam Smith in his Lectures some forty-five years later

As silver buys more gold abroad than at home, by sending abroad silver they bring gold in return, which buys more silver here than it does abroad. By this means a kind of trade is made of it, the gold coin increasing and the silver diminishing. Sometime ago a proposal was given in to remedy this, but it was thought so complex a case that they resolved for that time not to meddle with it. [Fay, 1935]

The direct consequence of this was that silver coin became increasingly unpopular, and in 1816, Gold was declared the “sole standard measure of value” [Fay, 1935], putting into the force of law what the markets had started doing a century earlier.

Shortly after defining the Gold Standard, Newton was caught up in the South Sea Bubble of 1720. Newton had been an early investor in the South Sea Company and in April, in the early days of the Bubble, he liquidated, doubling his money with a profit of £7,000 (roughly £700,000 in today’s terms). However, he was drawn into the mania again later that summer, and, according to his half-niece, the famously beautiful Catherine Barton, he lost £20,000 (roughly £2 million in today’s money!) [Kindleberger, 1996, p 28]. Craig notes that Catherine "was a hard woman”, and the ‘loss’ was never realised but rather the potential profit had Newton maintained his original holding and sold at the top of the market [Craig, 1946, p 112]. None the less, Newton was left to observe that

I can calculate the motion of the heavenly bodies, but not the madness of men.

Thursday, 28 July 2011

The macro-economics of August 2011 looks much the same as August 1971, but have we learnt anything about the markets over the past forty years?

Following the 1929 Crash and the consequent world-wide Depression governments around the world had devalued their currencies in order to make their products more competitive in foreign markets. These ‘beggar-thy-neighbour’ policies created a deflationary spiral that magnified the effects of the Crash. In 1944 the Allied powers met at Bretton–Woods, in New Hampshire, and agreed to fix the gold price of the main currencies, the US$ was fixed to gold at $35/oz, while other currencies were pegged to the dollar with the pound sterling being set at $4.03. Bretton–Woods also established the International Monetary Fund and World Bank.

By the late 1960s the Bretton–Woods system was beginning to creak as the Germans and Japanese exported to the Americans,while the U.S. poured money into th e war in Vietnam. As gold was sucked out of the U.S. the system began to look untenable. In 1971, foreign governments demanded that the U.S. honour its “promise to pay” and convert their dollar notes into gold, in July Switzerland converted $ 50 million into gold. There was an arbitrage, buy gold with dollars and then sell the gold for Deutsche Marks. On August 15, 1971 the U.S. President, Nixon, responded to these activities by abandoning the gold-standard, the “promise to pay”. Bretton Woods collapsed and foreign exchange rates stopped being
certain.

As a consequence of the collapse of the Bretton–Woods system of exchange rates central banks were forced to change the interest rates more frequently. In simplistic terms, the level of interest rates has two effects. If rates are low people will borrow from banks, who will create money for the economy and this may generate inflation which devalues a currency. If interest rates are high, and the currency stable, foreign investors will like to deposit their spare cash in banks paying the high rates of interest, raising demand for the currency. After 1972 interest rate policy became a key lever that governments had to control their economies. In the 27 years between 1945 and autumn 1972, when Bretton–Woods collapsed, the Bank of England changed its lending rate 43 times, in the 27 years after 1972, it changed them 223 times, about every 45 days. Finance had moved from a world of deterministic control to one of stochastic control, and people had to think more carefully about controlling their financial risks.

Business responded to this change in the economic environment by returning to the derivatives markets, using them to provide the tools to hedge the risks, whether as a borrower or a lender, of the fluctuating the interest rates. In the same year that Bretton-Woods collapsed, Nixon appointed William Casey, a spy and tax lawyer, as director of the Securities and Exchange Commission (SEC) and the path for the the derivatives exchanges was opened. A currency future had been created in New York in 1970, but had foundered. However when, on May 16, 1972, the Merc began trading futures on seven currencies the market for FX risk management was there and the Merc was rescued from the doldrums of the 1960s.

While futures or forward contracts, firm agreements to buy or sell an asset at a fixed price in the future, existed in an ethical and legal limbo, option contracts, contracts that gave the holder the right, but not the obligation, to trade were closer to the devil. As late as the 1960s officials of the SEC had compared options to thalidomide and marijuana and claimed that there had never been a case of market manipulation that did not involve options [MacKenzie, 2008, p 149]. Casey, and the SEC, cleared the Chicago Board of Options Exchange and it opened on April 26, 1973. Within days, the Journal of Political Economy, the house journal of the Chicago economists, published a paper, The Pricing of Options and Corporate Liabilities by Myron Scholes and Fischer Black.

The CBOT launched the first interest rate derivative in 1975, where the underlying was linked to mortgages, in 1976 the Merc introduced a future on 30-day U.S. Government Treasury bills, and CBOT launched a future on 30-year U.S. Treasury bonds in 1978. The London International Financial Futures Exchange opened in 1982 and in 1984 the equivalent of a stock–market index for interest rates, the London Interbank Offered Rate, LIBOR, began to be published, and futures, known, confusingly, as Eurodollar futures, began to be traded on the Merc based on this index.

It was not only the capital markets that were transformed in the 1970s. Up until 1973 the price of oil was set by the Railroad Commission of Texas, who controlled the oil production in Texas, and hence the oil price in the U.S., which as the world’s main oil consumer, effectively set the world price. Following the collapse of Bretton–Woods, the U.S. dollar’s value fell and as a consequence, the real income non-U.S. oil producers fell, and the Organisation of Oil Producing and Exporting Companies, OPEC, began to price their oil in gold and agree production quotas, setting the global–price. In 1973 the Middle-Eastern members of OPEC imposed an embargo on the west, following the defeat of the Syrian–Egyptian attack on Israel, and cut production, forcing the price of oil up. This, in-turn, prompted the development of alternative oil–provinces, notably the North Sea between the U.K. and Norway, which had been
previously un-economic. When this extra production hit the market, in the 1980s, just as demand fell, as consumers cut back consumption in response to higher-prices, and Iran and Iraq exceeded their quotas to fund their war (1980–1988), prices collapsed along with OPEC’s cohesiveness. In 1985 OPEC’s price-setting mechanism was abandoned, and another key economic input became a stochastic process, and in response, in 1988, the London based International Petroleum Exchange introduced the Brent oil futures contract.

Behind Black Monday, the failures of LTCM and The Equitable and the Credit Crisis of 2007–2008 is the fact that the financial world became stochastic in the aftermath of the collapse of Bretton–Woods,. The derivative markets did not spontaneously appear, they developed in response to the increased uncertainty in key economic drivers.

The world of 1980 was very different to that between 1918 and 1970 when exchange, rates, interest rates and commodity prices were being controlled by the great and the good. One view might be that the abandonment of Bretton–Woods had lead to the chaos of 1970s stagflation, another is that Bretton–Woods shattered under the strains of trying to confine the economy to a specific path. The derivative markets emerged in response to freeing the economy, the deterministic policies created impossible stresses in the global economy, and derivatives enabled risk–management in the resulting uncertainty.

The derivative markets were fundamentally different from the stock-markets, where decisions were made based on an investor’s judgement of the market fundamentals, and the core skills where in understanding economics and a company’s balance sheet, finance. The derivative markets were concerned with comparing the price differences between similar assets across different markets. It was not about the study of objects, but the relations between objects, and the derivative markets needed mathematical skills. In the aftermath of Black Monday significant numbers of applied mathematicians, physicists and engineers began working in the derivative markets, the ‘quants’ had arrived.

The events of August 2011 are not so different to those of August 1971, but then again these events are not so different to those of the 1690s!

Trading in stocks did not take off in England until after the Glorious Revolution of 1688. It is often assumed that this was because, as Geoffrey Poitras puts it, “William III was accompanied by an influx of Dutch persons and practises”. However a market does not create itself and, according to Anne Murphy, a historian who has worked as a currency trader, the root cause of the explosion of stock-market trading, and the accompanying boom, was the Nine Years War [Murphy, 2009, p 10–14], [Poitras, 2000, pp 281–285]. Murphy points to a contemporary account written by John Houghton in 1694

a great many Stocks have arisen since the war with France; for Trade being obstructed at Sea; few that had money were willing it should lie idle [Murphy, 2009, quoting on p 12]

It was not just the shortage of opportunities to participate in regular trade that stimulated the boom. England had grown wealthy under Charles II and alongside the increase in wealth was a growth in the financial services industry, involving life insurance and annuities, general insurance and the trade in the shares of the handful of joint-stock companies that existed at the time, such as the East India, Hudson Bay and Royal Africa [Murphy, 2009, p 12–19]. Evidence of this growth in financial services is provided by the 1673 Act of Common Council that looked to put an end to “usurious contracts, false Chevelance, and other crafty deceits” [Murphy, 2009, p 83].

The additional risks of sea trade resulting from the war with France, and the actions of privateers meant that merchants looked for domestic investment opportunities and the number of joint-stock companies exploded, and with more companies came a more active stock market. John Houghton describes how the market worked

The manner of managing Trade is this; the Monied Man goes amongst the Brokers (which are chiefly upon the Exchange [Alley], and at Jonathan’s Coffee House [the origins of the London Stock Exchange], sometimes at Garraway’s and at some other Coffee Houses) and asks how Stocks go? and upon Information, bids the Broker to buy or sell so many Shares of such and such Stocks if he can, at such and such Prizes [Poitras, 2000, quoting on p 288].

Brokers put buyers and sellers in touch with each other, for a commission but without actually taking possession of any asset. Alongside the monied men and brokers were the stock-jobbers or dealers, the speculators, providing liquidity in the market and trying to turn a profit from their trading. This dual-system, separating brokers from stock-jobbers, existed in London up until the ‘Big Bang’ of 1987.

In 1719 Daniel Defoe publishedRobinson Crusoe and wrote an articleThe Anatomy of ExchangeAlleyin which he described stockjobbing as

a trade founded in fraud, born of deceit, and nourished by trick, cheat, wheedle, forgeries, falsehoods, and all sorts of delusions; coining false news, this way good, this way bad; whispering imaginary terrors, frights hopes, expectations, and then preying upon the weakness of those whose imaginations they have wrought upon [Poitras, 2000, quoted in p 290]

An observation, mentioned by Defoe but more explicitly stated by Thomas Mortimer in 1761, concerned the type of person involved in stockjobbing. Mortimer makes the point that there are three types of stock-jobber, firstly foreigners, secondly gentry, merchants and tradesmen, and finally, and “by far the greatest number”, people

with very little, and often, no property at all in the funds, who job in them on credit, and transact more business in several government securities in one hour, without having a shilling of property in any of them, than the real proprietors of thousand transact in several years. [Poitras, 2000, quoted in p 291]

It was not only stocks that were being traded in the first half of the 1690s. Murphy estimates that around 40% of the trades between 1692 and 1695 were in stock options, that were being traded in order to manage the risks of stock trading. [Murphy, 2009, p 24–30] Evidence of the widespread use of options comes in 1720 when Colley Cibber, who would become Poet Laureate in 1730,, wrote a play,The Refusal (‘The Option’), describing the action in Exchange Alley

There you’ll see a duke dangling after a director; here a peer and ‘prentice haggling for an eighth; there a Jew and a parson making up the differences; there a young woman of quality buying bears of a Quaker; and there an old one selling refusals to a lieutenant of grenadiers [Ackroyd, 2001, p 308]

Clearly, in 1720 the public were familiar with the trading of derivatives, pretty much everyone was involved, and social, religious and political differences were forgotten in the markets.

The stock market boom that started in the late 1680s had gone bust by the middle of the next decade. At the time it was popular to blame stock-jobbers for destabilising the economy by either ramping worthless stock or undermining a going concern (depending on your point of view) [Murphy, 2009, p 33], while, more fundamentally, the stock market was attacked for turning “men away from honest and beneficial trades” [Murphy, 2009, p 68]. More rational explanations were that many of the joint-stock companies were mis-managed and the government’s need for cash sucked funds out of the market, causing prices to collapse [Murphy, 2009, p 35].

Anyone born before 1970, unless they have actually worked in the markets, find it difficult to understand the changes in the financial environment that had occurred after the collapse of Bretton–Woods. Derivatives would not start appearing on undergraduate courses in universities until the mid 1990s, and even then, for many of the lecturers in economics and finance educated in the post-war deterministic economies, they would be unfamiliar beasts. This meant that at the turn of the century there was a dire shortage of people with the skills to understand the complex world of derivatives [Tett, 2009, p 68], which required a unique grasp of financial theory, market practises, applied mathematics, probability and
statistics.

At the same time, some banks chose business managers as their chief executives, such as Fred Goodwin at the Royal Bank of Scotland or Andy Hornby at Halifax–Bank of Scotland, rather than ‘bankers’ bought up on the basic process, and the uncertainties, of converting credit into cash. The consequence of this was that some banks focused on efficient profit generation, the allocation of scarce resources, at the expense of monitoring the risks of their activities, managing an uncertain world. This manifested itself by firms buying in expertise, in the form of ‘black–box’ software systems to value the CDOs combined with external (or internal) consultants for advice. Some banks were not only out–sourcing their call centres, but their brains as well.

In the lead–up to the Crisis of 2007–2008, RBS sponsored sports-stars to the tune of 200 million pounds, in the same period they invested nothing in mathematics. J.P. Morgan was different, they developed, in–house, Value at Risk, CreditMetrics and employed David Li as he thought about using copulas to price CDOs. The quants that that they employed were able to develop these tools because they had a deep understanding of the markets and mathematics, and critically, how and where the mathematical models were weak and needed to be augmented. Not only did J.P. Morgan recognise the need for these skills, a feature shared by all the serious investment banks, but in disseminating their models they advertised
that their expertise was a fundamental component of “first class banking in a first class way”.

The benefit of J.P. Morgan’s approach is described by Gillian Tett in her account of the Credit Crisis, Fool’s Gold. The background is it is 2005–2006 and J.P. Morgan’s shareholders are putting the bank’s managers under intense pressure to mimic the revenues being reported by other investment banks, who were actively investing in CDOs of MBS.

[The J.P. Morgan chief executive] made it clear that he wanted a mortgage production line, so Winters had duly asked his staff to re–examine how to create a profitable business selling mortgage–based CDOs.

When they crunched the numbers, though, they ran into a problem. “There doesn’t seem to be a way to make money on these structures,” Brian Zeitlin, one of the bankers who worked in the CDO division reported. …

Reluctantly, Winters told the J.P. Morgan management should not open the spigots on its pipeline after all. The decision was greatly frustrating, though. The other banks were pushing JPMorgan Chase further and further down the league tables largely due to the bonanza from their mortgage pipelines. So were they just ignoring the risks? Or had they found some alchemy that made the economics of their
machines work? [Tett, 2009, pp 148–151]

The J.P. Morgan quants had taken the prices the traders were observing in the market and reverse engineered them, just like they did with the Black–Scholes pricing formula, extracting the key parameter, ρ. When they told the traders that the basis of the prices in the market was ρ = 0.3, the traders could not believe it. A correlation of ρ = 0.3 implies that there is only a small linkage between defaults, reflecting the fact that if BP went bust it did not mean that Tesco would follow suite. But anyone who had seen an economic downturn would be familiar with whole streets being derelict, the correlation of mortgage defaults was unknown, but not insignificant.

There is another aspect to the approach taken by the banks that weathered the storms of 2007–2008. While there is frequently the claim that the Credit Crisis was a global phenomenon, it was not. Asian banks were unaffected and British and American banks suffered far more than French or German banks. The explanation that banks were not as involved as RBS or Merrill Lynch is not a satisfactory answer (BNP Paribas, SocGen and Deutsche Bank were all heavily involved in credit derivatives. [FCIC, 2011, Fig 20.4, for example]). U.S. bankers have been known to suggest that the non Anglo-Saxon banks played fast and loose with accounting rules, not declaring their losses on credit derivatives. The response to this criticism from French mathematicians is typically Gallic, and Cartesian, “They thought the models were wrong before August 2007, they were certain they were wrong after August 2007, so why should they post losses that they were certain were wrong.”. This point was highlighted by a quote that appeared in TheEconomistmagazine, in January 2008 in relation to a fraud at the French bank, SocGen

In common with other French banks, SocGen was also thought by many to take an overly mathematical approach to risk. “ ‘It may work in practice but does it work in theory?’ is the stereotype of a French bank,” says one industry consultant. (‘No Defense’, The Economist, 31 January 2008.)

The bankers at J.P. Morgan, along with French risk–managers, kept in mind Hume’s observation that “it is never contradictory to deny matter of fact”. Bankers, like all scientists, must use their intellect and constantly ask themselves the questions ‘why’ and ‘how’ to give them the foresight not to act recklessly.

The common thread linking financial crises since Bretton-Woods, Black Monday, the Equitable, the super–portfolio that bought down LTCM, the tech–bubble of 2000 and the Credit Crisis was not the collapse of Bretton–Woods but the adoption of standardised approaches to finance. Had the majority of traders, bankers and regulators thought like mathematicians, or French risk managers, and asked themselves, in a Cartesian manner, “how do I know what I think I know is true?”, then the crises might have been avoided. Banning speculative trading in deriviatives is simplistic, and not the answer.

References

P. Ackroyd. London: The Biography. Vintage, 2001.

FCIC. The Financial Crisis Inquiry Report. Technical report, The National Commission
on the Causes of the Financial and Economic Crisis in the United States, 2011.

D. MacKenzie. An Engine, Not a Camera: How Financial Models Shape Markets. The
MIT Press, 2008.

A. L. Murphy. The Origins of English Financial Markets. Cambridge University Press,
2009.

G. Poitras. The Early History of Financial Economics, 1478–1776. Edward Elgar, 2000.

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About Me

I am a Lecturer in Financial Mathematics at Heriot-Watt University in Edinburgh. Heriot-Watt was the first UK university to offer degrees in Actuarial Science and Financial Mathematics and is a leading UK research centre in the fields.

Between 2006-2011 I was the UK Research Council's Academic Fellow in Financial Mathematics and was involved in informing policy makers of mathematical aspects of the Credit Crisis.